Retraction Approach to CPS Transform

We study the continuation passing style (CPS) transform and its generalization, the computational transform, in which the notion of computation is generalized from continuation passing to an arbitrary one. To establish a relation between direct style and continuation passing style interpretation of sequential call-by-value programs, we prove the Retraction Theorem which says that a lambda term can be recovered from its continuationized form via a-deenable retraction. The Retraction Theorem is proved in the logic of computational lambda calculus for the simply typable terms.